Cryptoasset networks: Flows and regular players in Bitcoin and XRP

Cryptoassets flow among players as recorded in the ledger of blockchain for all the transactions, comprising a network of players as nodes and flows as edges. The last decade, on the other hand, has witnessed repeating bubbles and crashes of the price of cryptoassets in exchange markets with fiat currencies and other cryptos. We study the relationship between these two important aspects of dynamics, one in the bubble/crash of price and the other in the daily network of crypto, by investigating Bitcoin and XRP. We focus on “regular players” who frequently appear on a weekly basis during a period of time including bubble/crash, and quantify each player’s role with respect to outgoing and incoming flows by defining flow-weighted frequency. During the most significant period of one-year starting from the winter of 2017, we discovered the structure of three groups of players in the diagram of flow-weighted frequency, which is common to Bitcoin and XRP in spite of the different nature of the two cryptos. By examining the identity and business activity of some regular players in the case of Bitcoin, we can observe different roles of them, namely the players balancing surplus and deficit of cryptoassets (Bal-branch), those accumulating the cryptoassets (In-branch), and those reducing it (Out-branch). Using this information, we found that the regime switching among Bal-, In-, Out-branches was presumably brought about by the regular players who are not necessarily dominant and stable in the case of Bitcoin, while such players are simply absent in the case of XRP. We further discuss how one can understand the temporal transitions among the three branches.


Appendix A Granger Causality Analysis of Price and Number of Players
Our VAR (vector auto regressive) model describes the time evolution of the log change rate of the price of cryptoassets, the number of IN players, and the number of BAL players. In the following, we denote the log change rate of the price of cryptoasset by y t and the log change rate of the number of IN players and BAL players by x t . As the evaluation criterion for the VAR model, we use the mean square error where U is the information used in the model andŷ t is the prediction by the model defined byŷ In Granger causality analysis, x t is interpreted to be the cause of y t when the following relation is satisfied. It also interprets x t as being the instantaneous cause of y t when the relation is satisfied. Here X (t − 1) is the information set about past x t , and Y(t − 1) is the information set about past y t . Granger causality analysis requires a stationary time series process. We conducted a unit root test to determine if it is a stationary process. The obtained augmented Dickey-Fuller statistic and the p-values are shown in Tables S1 and S2. The p-values were less than 5% for all variables and periods except where underlined. These results confirm that the overall process is stationary.
We performed a Granger causality analysis to examine the significance of the effect of changes in the number of players x t on price changes y t . Tables S3,  S4, S5, and S6 show the F statistic and the p-value, which is the probability of hitting a value greater than the F statistic in an F distribution with two degrees of freedom df 1 and df 2 for active IN player, active BAL player, regular IN player, and regular BAL player, respectively, obtained in the Granger causality analysis. For all variables and periods, the p-values are very large. These results indicated in the tables mean that x t is not interpreted to be the cause of y t for all cases.
In addition, We performed an instantaneous causality analysis to examine the significance of the changes in the number of players x t as being the instantaneous cause of price changes y t . Tables S7, S8, S9, and S10 show the χ 2 value and the p-value, which is the probability of hitting a value greater than the χ 2 value in an χ 2 distribution with degree of freedom df for active IN player, active BAL player, regular IN player, and regular BAL player, respectively, obtained in the instantaneous causality analysis. The p-values show sufficiently small values for all variables and periods except where underlined. These results indicated in the tables mean that the x t is interpreted to be the instantaneous cause of y t for all cases.
In summary, x t is not the cause of y t in the Granger sense. Including x t in the model does not improve the prediction accuracy of y t . On the other hand, x t is a instantaneous cause of y t . However, instantaneous causality does not lead to more accurate forecasts. These results indicate that it is difficult to forecast the prices of cryptoasset using the number of players. These results support the results discussed in Table 5, Table 6, and Table 7.

Appendix B Identity of Bitcoin Users
This supplement explains how we obtain the identity and classification of business activities of regular playes for Bitcoin.
In the case of Bitcoin, we employed a simple but useful method, proposed by [1] and widely used in the literature, to identify users from wallets or addresses by identifying a set of multiple input of addresses in each transaction as a user in the way that the identification must be consistent in the entire history of all the transactions up to a certain point in time (see [2] for technical details). Our study is based on this method and on the entire history from the genesis block (first block issued on January 9, 2009) until the block of height 693,999 (issued on August 3, 2021).
As a result, among more than 700 million different addresses, 500 million of them were identified as 73 million users. A user corresponds to two or more addresses by the above mentioned method of identification. A user can possess a large number of addresses; the largest one corresponds to the case of 13 million addresses for a single user. We denote such users with two or more addresses by type A. The rest of unidentified addresses are regarded as users individually, denoted by type B. We label a user of type A by a user ID, sequential and increasing with the number of identified addresses, e.g. 0000012345, while a user of type B is labeled by its address, e.g. 3CjqmbuRA1LEWmLHiWoSWHcWuTEVPfU24P.
Because of the very nature of anonymity inherent in the technology of blockchain, it is difficult to obtain the information of actual names of those users. However, in the case of agents who are doing business activities such as exchanges, services, gambling, and mining, it is known that one can obtain the identify of users. Such information could be useful for our study, even if not complete and exhaustive, as we found in our paper. In fact, WalletExplorer.com [3] is a well known web site providing information about identity of addresses in Bitcoin blockchain. The site merges addresses together, if they are part of the same wallet, and also identifies wallets with actual names. According to the site, the method to merge addresses is precisely the same as [1], which is the one we employed in our paper. Additionally, the identification of actual names is done by WalletExplorer.com as follows (quoted from the web site): In most of the cases, I registered to service, made transaction(s) and saw which wallet bitcoins were merged with, or from which wallet it was withdrawn. There is probably no easier way how to discover names other than this. Please note that the name database is not updated, so it does not contain newer exchanges (or newer wallets of existing exchanges).
We matched our data with this useful information to obtain the identity and classification of business activities for the users of type A. We were successful in unravel the identity of 369 users in this way, which are used in the main body of our paper. Table S11 is the classification into exchanges, services, gambling, historic, and mining pools. Table S12 is the complete list of the matching.